BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Emmanuele Pavia (SISSA\, Italy) DTSTART:20240327T130000Z DTEND:20240327T140000Z DTSTAMP:20260423T024800Z UID:LAGOON/92 DESCRIPTION:Title: Sheaves of categories over topological and coaffine stacks\nby Emmanue le Pavia (SISSA\, Italy) as part of Longitudinal Algebra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nStarting from any sufficiently nic e topological space X\, one can produce two different (derived) stacks def ined over a field k of characteristic 0: the Betti stack X_B\, which bears information on the underlying homotopy type of X\, and the coaffine stack cSpec(C*(X\; k)) on the commutative algebra C*(X\; k) of k-valued singula r cochains on X\, which behaves as the affinization of the Betti stack X_B . In this talk\, I shall apply the technical machinery of sheaves of (∞- )categories on derived stacks as developed in Gaitsgory’s work to the ca se of Betti stacks and their associated coaffine stacks. We shall see how sheaves of categories on X_B are intimately related to categorified local systems over the original space X and to homotopy-coherent actions of topo logical groups on k-linear ∞-categories. At the very end\, I shall brief ly describe how sheaves of categories on X_B and on cSpec(C*(X\; k)) inter act\, and how such interaction can be interpreted as an instance of higher Koszul duality. This talk is based on upcoming joint work with J. Pascale ff and N. Sibilla.See abstract under 'Paper link' below.\n\nLive stream: h ttps://uni-koeln.zoom.us/j/91875528987?pwd=US8wdjNrWjl5dXNQSVRzREhoRE1PUT0 9\n\nMeeting ID: 918 7552 8987\nPassword: LAGOON\n LOCATION:https://researchseminars.org/talk/LAGOON/92/ END:VEVENT END:VCALENDAR